[Bud Cline]

First you MUST verify the joist spacing and the subfloor thickness before you can get any straight answers for your questions. Jumping the gun accomplishes nothing.

Is it the same plywood that the parquet is on? If so, 1/4 in cement board on top of the subfloor would work good.

Here we go again Stancheski. If the subfloor is in fact only 3/4" thick, and the joists are in fact spaced 24" on center, adding 1/4" cement board isn't the way to go. The deflection-between-the-joists will be much too great to support the tile properly. That is a prescription for cracking tile and grout in the near future.

Let's get some facts together before we go off screwing up someone's new flooring.

 

[Bud Cline]

I don't waste any time on trying to match elevations perfectly. It takes a lot of time and money and varying transitions are common and don't hurt a thing. If person wants to be anal about it then they can spend their time figuring how to get it perfect.

Doesn't matter to me if wood or tile goes first. I always use a metal edging at the juncture and I would rather be there first. This way I'm not apologizing for some dumb ass wood installer that can't square-up and match end cuts in his floor. A lot of those guys depend on lapping juncture materials to cover their butts. I don't want to apologize for his errors.